Conditioned pressure spectra and coherence measurements in the core of a turbofan engine

Multiple and partial coherence functions and the corresponding conditioned coherent output spectra are computed between fluctuating pressures measured at two locations within the tailpipe of a turbofan engine and far-field acoustic pressure. The results are compared with the ordinary coherent output spectrum as obtained between a single tailpipe pressure measurement and the far-field acoustic pressure. The comparison indicates apparent additional "coherent output" (i.e., core-noise) beyond that detectable with an ordinary coherent measurement, thus suggesting the tailpipe as a core-noise source region. Further evidence suggests, however, that these differences may be attributed to the presence of transverse acoustic modes in the tailpipe and that the tailpipe is not, in fact, a significant source region

Acoustic modal analysis of a full-scale annular combustor

An acoustic modal decomposition of the measured pressure field in a full scale annular combustor installed in a ducted test rig is described. The modal analysis, utilizing a least squares optimization routine, is facilitated by the assumption of randomly occurring pressure disturbances which generate equal amplitude clockwise and counter-clockwise pressure waves, and the assumption of statistical independence between modes. These assumptions are fully justified by the measured cross spectral phases between the various measurement points. The resultant modal decomposition indicates that higher order modes compose the dominant portion of the combustor pressure spectrum in the range of frequencies of interest in core noise studies. A second major finding is that, over the frequency range of interest, each individual mode which is present exists in virtual isolation over significant portions of the spectrum. Finally, a comparison between the present results and a limited amount of data obtained in an operating turbofan engine with the same combustor is made. The comparison is sufficiently favorable to warrant the conclusion that the structure of the combustor pressure field is preserved between the component facility and the engine

Lip noise generated by flow separation from nozzle surfaces

The results of a series of experiments, performed to investigate flow separation and classic lip noise and to aid in understanding aeroacoustic noise generation are presented. Several types of nozzle-lip configurations were used to study the high frequency noise generated by small regions of flow separation at the nozzle lip. These included coaxial nozzles, and circular and slot nozzles with splitter plates. The jet flow velocity was varied and far field noise was measured for all nozzle-lip geometries (coaxial and splitter plate). The effect of a velocity difference across the lip of the coaxial nozzle and the splitter plate on the far field noise was also measured. Finally, an effort was made to find means to reduce the high frequency noise caused by flow separation at the lip

Core noise measurements from a small, general aviation turbofan engine

As part of a program to investigate combustor and other core noises, simultaneous measurements of internal fluctuating pressure and far field noise were made with a JT15D turbofan engine. Acoustic waveguide probes, located in the engine at the combustor, at the turbine exit and in the core nozzle wall, were used to measure internal fluctuating pressures. Low frequency acoustic power determined at the core nozzle exit corresponds in level to the far field acoustic power at engine speeds below 65% of maximum, the approach condition. At engine speeds above 65% of maximum, the jet noise dominates in the far field, greatly exceeding that of the core. From coherence measurements, it is shown that the combustor is the dominant source of the low frequency core noise. The results obtained from the JT15D engine were compared with those obtained previously from a YF102 engine, both engines having reverse flow annular combustors and being in the same size class

Combustor fluctuating pressure measurements in engine and in a component test facility: A preliminary comparison

In a program to investigate combustor noise, measurements were made with a YF-102 engine of combustor internal fluctuating pressure and far field noise. The relationship of far field noise to engine internal measurement was ascertained. The relationships between combustor internal measurements obtained in an engine and those obtained in a component test facility were established by using a YF-102 combustor, instrumented identically with that used in the engine tests. The combustor was operated in a component test facility over a range of conditions encompassing engine operation. A comparison of the directly measured spectra at corresponding locations in the two tests showed significant differences. The results of two point signal analyses within each combustor, were similar for both tests, indicating that the internal dynamics of the combustor as an acoustic source are preserved in a component test facility

Noise tests on an externally blown flap with the engine in front of the wing

Noise tests were conducted with a nozzle exhausting over a small scale model of an externally blown flap (EBF) lift-augmentation system, with exhaust impingement on the wing leading edge. Two series of tests were conducted: with wing leading edge inside the nozzle; and with leading edge set back from the nozzle exit plane 1 diameter on the jet axis. The results indicated no significant differences in spectral shape, level, or directivity pattern. Static lift and thrust tests were conducted on the same model indicated considerable flow attachment on both configurations, with slightly greater attachment and turning for the wing outside the nozzle. Finally, a comparison with engine-above- and engine-below-the-wing EBF's tested by previous investigators shows the acoustic performance of the configurations tested for this report to lie between the other two

Acoustical modal analysis of the pressure field in the tailpipe of a turbofan engine

The results of a modal analysis of the pressure field in the tailpipe of a turbofan engine are presented. Modal amplitudes, at the tailpipe inlet and exit, are presented, as a function of frequency, for several operating conditions. The modal amplitudes were obtained using an optimization routine to obtain a best fit between measured cross spectra and an analytical expression for the cross spectra between pressures at circumferentially spaced locations. The measured pressure field was decomposed into a set of five modal amplitudes corresponding to the (0,0), (1,0), (2,0), (3,0), and (4,0) modes. The analysis was limited to frequencies below 1500 Hz where higher order modes are cutoff. The results of the analysis showed that at low frequencies, up to the cuton frequency of the (1,0) mode, the (0,0) mode (plane wave) dominated the pressure field. The frequency range from the cuton of the (1,0) mode to the cuton of the (2,0) mode was dominated by the (1,0) mode. The (2,0) mode dominated from its cuton frequency to the upper limit of the analysis, i.e., 1500 Hz. The contribution of modes other than the dominant mode was usually small

Agnostic Membership Query Learning with Nontrivial Savings: New Results, Techniques

(Abridged) Designing computationally efficient algorithms in the agnostic learning model (Haussler, 1992; Kearns et al., 1994) is notoriously difficult. In this work, we consider agnostic learning with membership queries for touchstone classes at the frontier of agnostic learning, with a focus on how much computation can be saved over the trivial runtime of 2^n$. This approach is inspired by and continues the study of ``learning with nontrivial savings'' (Servedio and Tan, 2017). To this end, we establish multiple agnostic learning algorithms, highlighted by: 1. An agnostic learning algorithm for circuits consisting of a sublinear number of gates, which can each be any function computable by a sublogarithmic degree k polynomial threshold function (the depth of the circuit is bounded only by size). This algorithm runs in time 2^{n -s(n)} for s(n) \approx n/(k+1), and learns over the uniform distribution over unlabelled examples on \{0,1\}^n. 2. An agnostic learning algorithm for circuits consisting of a sublinear number of gates, where each can be any function computable by a \sym^+ circuit of subexponential size and sublogarithmic degree k. This algorithm runs in time 2^{n-s(n)} for s(n) \approx n/(k+1), and learns over distributions of unlabelled examples that are products of k+1 arbitrary and unknown distributions, each over \{0,1\}^{n/(k+1)} (assume without loss of generality that k+1 divides n)

Acoustic tests of a 15.2 centimeter-diameter potential flow convergent nozzle

An experimental investigation of the jet noise radiated to the far field from a 15.2-cm-diam potential flow convergent nozzle has been conducted. Tests were made with unheated airflow over a range of subsonic nozzle exhaust velocities from 62 to 310m/sec. Mean and turbulent velocity measurements in the flow field of the nozzle exhaust indicated no apparent flow anomalies. Acoustic measurements yielded data uncontaminated by internal and/or background noise to velocities as low as 152m/sec. Finally, no significantly different acoustic characteristics between the potential flow nozzle and simple convergent nozzles were found